Wrinkling of graphene because of the thermal expansion mismatch between graphene and copper

Well-defined bundles of wrinkles are observed on the graphene-covered copper by using atomic force microscopy after chemical vapor deposition process. Their numerical analyses are performed by employing a set of formula deduced from classical elasticity theory of bent thin films with clamped boundary conditions. Here they are imposed by the banks of trenches associated with the reconstructed copper substrate surfaces, which suppress lateral movements of graphene monolayers and induce local biaxial stress. The wrinkling wavelength (lambda) and amplitude (A) are both measured experimentally (lambda = 100-160 nm and A = 2.5-3 nm) and calculated numerically (lambda = 167 nm and A = 3.0 nm) and found to be in good agreement. Wrinkle formation is attributed to the nonhydrostatic compression stresses induced on the graphene by the linear thermal expansion coefficient difference between graphene and copper during cooling. These mismatch stresses, which are varying strongly with the temperature, create temperature-dependent wrinkling wave formation that decreases in wavelength and increases in amplitude upon cooling below the crossover temperature of 1233 K, at which both values of linear thermal expansion coefficient are equal